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An absorbing state is a state that, once entered, cannot be left. It is characterized by a transition probability of 1 to itself.

Conditions: Transition probability from the state to itself must be exactly 1.; The system eventually enters an absorbing state if reachable.

An absorbing state is a state that, once entered, cannot be left. It is characterized by a transition probability of 1 to itself.

Conditions: Transition probability from the state to itself must be exactly 1.; The system eventually enters an absorbing state if reachable.

The stationary distribution describes the long-run frequency of visiting each state in a Markov chain. It does not mean the system stops moving; rather, it represents a dynamic equilibrium where the probability flows between states balance out.

Conditions: The Markov chain has reached its long-run behavior.; The chain is ergodic (irreducible and aperiodic) for a unique stationary distribution to exist.

The stationary distribution describes the long-run frequency of visiting each state in a Markov chain. It does not mean the system stops moving; rather, it represents a dynamic equilibrium where the probability flows between states balance out.

Conditions: The Markov chain has reached its long-run behavior.; The chain is ergodic (irreducible and aperiodic) for a unique stationary distribution to exist.

The Markov property is the defining assumption of a Markov chain: the future depends on the current state, but not on the full past. It does not mean history is irrelevant; rather, it means that all relevant historical information is summarized by the present state.

Conditions: The process satisfies the Markov property.; The current state contains all information needed to determine future transition behavior.

The Markov property is the defining assumption of a Markov chain: the future depends on the current state, but not on the full past. It does not mean history is irrelevant; rather, it means that all relevant historical information is summarized by the present state.

Conditions: The process satisfies the Markov property.; The current state contains all information needed to determine future transition behavior.